Many production and observation wells have boreholes that are cased. Thus, monitoring changes in formation stresses caused by either depletion or injection of fluids at such wellsites may involve analyzing and inverting sonic data acquired in cased boreholes. However, the characteristics of the sonic data acquired at an array of receivers in a cased borehole can be affected by the quality of bonds between the steel casing and cement annulus, as well as the bonds between the cement annulus and the formation. As such, the processing and interpretation of sonic data obtained from cased boreholes can be more challenging than in open holes because of for example, interference from the casing arrivals, reduced sensitivity of sonic velocities to changes in formation properties, etc.